A fixed point index approach to Krasnosel'skii-Precup fixed point theorem in cones and applications

2022/06/21 by Jorge Rodríguez López, Rodríguez-López, Jorge · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2206.10497

openalex publication_date 2022/06/21 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

Abstract

We present an alternative approach to the vector version of Krasnosel'skii compression-expansion fixed point theorem due to Precup, which is based on the fixed point index. It allows us to obtain new general versions of this fixed point theorem and also multiplicity results. We emphasize that all of them are coexistence fixed point theorems for operator systems, that means that every component of the fixed points obtained is non-trivial. Finally, these coexistence fixed point theorems are applied to obtain results concerning the existence of positive solutions for systems of Hammerstein integral equations and radially symmetric solutions of (p₁,p₂)-Laplacian systems.

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• On Krasnosel'skii-Precup fixed point theorem and eigenvalue criteria for existence of positive solutions

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